The Labour peer who led the Lords rebellion against legal aid cuts has condemned the measures for "picking on people who can't defend themselves" and announced he is standing down from frontbench duties.

Lord Bach, a minister in the last government and then shadow spokesman on legal aid, described the legislation as a "bad day for the British justice system". The former criminal barrister said he had stayed on to fight the bill but would now go to the backbenches.

"I was determined to see this through," he said. "It's such a rotten bill. This demeans our justice system and therefore our country. What we now do is to encourage rich foreign litigants to come to this country and [fight their cases in court]. But we take away from the poor their access to justice. What a scandal that is.

"I shall go on the backbenches to make sure that social welfare causes are not forgotten. The Lords didn't like this bill at all. They spotted it for what it was. It was picking on people who can't defend themselves."

He added: "As a consequence of this bill, and those on welfare reform and the NHS, there are many in the Lords who are very disturbed by the way these issues have been approached. There was a powerful coalition of cross-benchers and Labour. These [cuts] are wicked, wicked in an old-fashioned sense."

The bill suffered 14 defeats in the Lords, the highest number for many years. A few of the most contentious amendments were accepted by the coalition, but most were rejected on the grounds that the bill was primarily a financial measure on which the Commons could overrule the Lords' objections.

The Legal Aid, Sentencing and Punishment of Offenders Act, which received royal assent this week, is intended to save £350m from the Ministry of Justice's annual civil legal aid budget.

The cuts, which remove support for most cases involving housing, welfare, medical negligence, employment, debt and immigration, will come into force next year.

Opponents fear that law centres and citizens advice bureaux will lose their main source of funding and will increasingly have to charge clients for the advice they provide. The government has announced a £20m fund for the advice sector to compensate for expected losses.

It will take time to assess the impact of the bill. Some lawyers are likely to challenge the availibility of legal aid for specific cases, and others may decide to take on cases on the less attractive no-win-no-fee terms now available. Many claims may simply no longer be viable to bring to court.

Labour is bitter that many Liberal Democrats who voiced concerns did not follow through by voting against key divisions in the bill. "These changes would not have gone through if the [Lib Dem peers] had decline to vote for them on the basis of principle," Bach said. "They spoke with one voice then voted with a completely different voice."

Labour is cautious about promising to repeal legal aid cuts. Andy Slaughter, Labour's justice spokesman, said: "It's very difficult to say where we will be in 2015 and … how much money we will have."

But he criticised the government for "cynical" timing in choosing to target civil legal aid. "It's an important safety net," he said. "We now have major cuts to get people off benefit just at the time they don't have [legal aid]. It covers up mistakes made. This is a cynical approach to government."

The Ministry of Justice welcomed the legislation passing into law. It said the act would focus legal aid on cases "where legal help is most needed, where people's life or liberty is at stake or they are at risk of serious physical harm, face immediate loss of their home or their children may be taken into care, [while] reducing the £2.1bn per year legal aid bill for England and Wales."

It added: "Legal aid will always be available in criminal and childcare proceedings, and in some private family or civil cases, such as claims by victims of domestic violence against their former partners. But legal aid will no longer be available where legal help is not absolutely necessary – for example where foreign students want help to fill in visa applications, or where a landlord and tenant are arguing over routine maintenance."

The MoJ said reform of no-win-no-fee lawsuits would "stop lawyers being able to double their fees through payments which have driven up insurance premiums and left local authorities, hospitals and businesses threatened by high legal costs".